Develops a quantitative flatness framework to obstruct Fourier restriction, L^p-improving, and Fourier decay estimates for measures, applied to bound Fourier dimensions of surfaces, curves, Patterson-Sullivan measures, and self-affine sets.
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Polynomial Fourier decay holds for images of self-similar measures under sufficiently nonlinear real-analytic maps.
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Quantitative flatness and obstructions in Fourier analysis
Develops a quantitative flatness framework to obstruct Fourier restriction, L^p-improving, and Fourier decay estimates for measures, applied to bound Fourier dimensions of surfaces, curves, Patterson-Sullivan measures, and self-affine sets.
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Fourier transform of nonlinear images of self-similar measures: qualitative aspects
Polynomial Fourier decay holds for images of self-similar measures under sufficiently nonlinear real-analytic maps.